The present embodiments relate to reconstruction of emission tomography, such as positron emission tomography (PET).
The uptake function of blood, such as within the brain, may be difficult to measure. The input function may be measured by arterial blood sampling, but blood sampling is invasive. The input function may be estimated using PET in the image or projection domains. However, the input function is best assessed when the contrast is high compared to adjacent tissue uptake. For fluorodeoxyglucose (FDG), the contrast peaks at around 30-40 seconds following injection.
To measure FDG uptake at the contrast peak, the image-domain input function may be obtained by reconstruction of individual short frames (1 or 2 sec frame durations). The detected events during this short period are used for reconstruction. However, the resulting images are very noisy due to the lack of information in the projection (sinogram), resulting in poor delineation of the blood vessels.
Iterative reconstruction with adding regularization and prior information of the shape of the input function may improve the noise. However, these individual frame-based methods have problems due to a positivity constraint of iterative reconstruction, resulting in Poisson noise. This kind of peak noise prevents distinction between blood vessels and tissues. To solve these noise problems, four dimensional reconstruction has been proposed and works well for tissue since the kinetic constant is long enough compared to the very short sampling. The technique fails for blood input function since the necessary basis function to describe the time correlation (i.e., delta function corresponding to individual frame reconstruction) is too short.